Let f (x) = 4x - 5 and g (x) = 3x + 7. find f (x) + g (x) and state its domain.

We are given the functions:

f (x) = 4 x - 5 - - - > 1

g (x) = 3 x + 7 - - - > 2

To find for the value of f (x) + g (x), all we have to do is to add equations 1 and 2:

f (x) + g (x) = 4 x - 5 + 3 x + 7

f (x) + g (x) = 7 x + 2 = y

In this case, for any real number value assign to x, we get a real number value of y. This is because the function is linear.

Therefore the domain of the function is all real numbers.